Lasing eigenvalue problems (LEPs) are non-conventional eigenvalue problems involving the frequency and gain threshold at the onset of lasing directly. Efficient numerical methods are needed to solve LEPs for the analysis, design and optimization of microcavity lasers. Existing computational methods for two-dimensional LEPs include the multipole method and the boundary integral equation method. ...

A novel hybrid boundary element-finite element scheme which is accelerated by an adaptive multi-level fast multipole algorithm is presented to simulate 3D plane wave electromagnetic induction responses in the Earth. The remarkable advantages of this novel scheme are the complete removal of the volume discretization of the air space and the capability of simulating large-scale complicated geoele...

We present a framework using the Quantized Tensor Train (QTT) decomposition to accurately and efficiently solve volume and boundary integral equations in three dimensions. We describe how the QTT decomposition can be used as a hierarchical compression and inversion scheme for matrices arising from the discretization of integral equations. For a broad range of problems, computational and storage...